| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 9216.6-a1 |
9216.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.6 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{8} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.345364298$ |
1.772928762 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 8\) , \( 8\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+8{x}+8$ |
| 9216.6-a2 |
9216.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.6 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$4.690728597$ |
1.772928762 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-2{x}$ |
| 9216.6-a3 |
9216.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.6 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{2} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.345364298$ |
1.772928762 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -17\) , \( -33\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-17{x}-33$ |
| 9216.6-a4 |
9216.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.6 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{2} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$2.345364298$ |
1.772928762 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -32\) , \( 60\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-32{x}+60$ |
| 9216.6-b1 |
9216.6-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.6 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{12} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.186168360$ |
$1.123705634$ |
3.795339664 |
\( \frac{1906624}{729} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 41\) , \( -59 a + 9\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+41\right){x}-59a+9$ |
| 9216.6-b2 |
9216.6-b |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.6 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.372336720$ |
$2.247411269$ |
3.795339664 |
\( \frac{82881856}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 36\) , \( -76 a + 20\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+36\right){x}-76a+20$ |
| 9216.6-c1 |
9216.6-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.6 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{12} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.186168360$ |
$1.123705634$ |
3.795339664 |
\( \frac{1906624}{729} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 41\) , \( 59 a - 9\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+41\right){x}+59a-9$ |
| 9216.6-c2 |
9216.6-c |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.6 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.372336720$ |
$2.247411269$ |
3.795339664 |
\( \frac{82881856}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 36\) , \( 76 a - 20\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+36\right){x}+76a-20$ |
| 9216.6-d1 |
9216.6-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.6 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{8} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.345364298$ |
1.772928762 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 8\) , \( -8\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+8{x}-8$ |
| 9216.6-d2 |
9216.6-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.6 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{4} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$4.690728597$ |
1.772928762 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-2{x}$ |
| 9216.6-d3 |
9216.6-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.6 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{2} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.345364298$ |
1.772928762 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -17\) , \( 33\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-17{x}+33$ |
| 9216.6-d4 |
9216.6-d |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.6 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{2} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.345364298$ |
1.772928762 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -32\) , \( -60\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-32{x}-60$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
